%I #21 Jul 29 2019 11:52:25
%S 1,3,8,22,66,170,210,490,510,930,1470,2130,2910,3810,5406,5970,7230,
%T 7590,10110,12306,13470,14322,17310,17490,23142,26430,29010,32430,
%U 37470,42546,44814,49170,58674,69330,73830,86610,87780,96690
%N Numbers k such that usigma(k) is a square and sets a new record for such squares.
%H Amiram Eldar, <a href="/A064443/b064443.txt">Table of n, a(n) for n = 1..250</a> (terms 1..100 from Harry J. Smith)
%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger@n); um = 0; s = {}; Do[u = usigma[n]; If[IntegerQ@Sqrt[u] && u > um, um = u; AppendTo[s, n]], {n, 1, 10^5}]; s (* _Amiram Eldar_, Jul 29 2019 *)
%o (PARI) usigma(n, s=1, fac, i) = fac=factor(n); for(i=1,matsize(fac)[1],s=s*(1+fac[i,1]^fac[i,2])); return(s); a=0; j=[]; for(n=1,10^5,x=usigma(n); if(issquare(x),b=x; if(b>a,a=b; j=concat(j,n)))); j
%o (PARI) usigma(n)= { local(f,s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) } { n=a=0; for (m=1, 10^9, if (issquare(b=usigma(m)), if(b>a, a=b; write("b064443.txt", n++, " ", m); if (n==100, break))) ) } \\ _Harry J. Smith_, Sep 14 2009
%Y Cf. A034448.
%K nonn
%O 1,2
%A _Jason Earls_, Oct 01 2001